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Yes, frequency spikes like that are normal - it is a feature of these CPU. Intel calls this "Turbo Boost", and allows for for example your 2.8 Ghz Core i7 processor to Turbo Boost up to 3.8 Ghz for peak loads. The CPU automatically handles Turbo Boost, and it is only allowed to happen when all necessary conditions are fulfilled - amongst those are that the temperature is not too high, the power consumption is not too high, and not all cores are actively "busy".

Temperature spikes are also perfectly normal. When the CPU is idle, it uses less power - and thus has a lower temperature than when fully utilizes. The maximum temperature you have recorded is 90 degrees - this is perfectly normal and well within the operating temperature range of the CPU.

As for the abrupt shutdowns of the computer - there are multiple possible causes of this - you haven't really demonstrated that overheating has anything to do with your problem, but check your fans and generally that the machine isn't full of dust. Other possible causes could be battery problems, a faulty sensor, etc.

Thanks a lot for your answer. Very useful. The reasons I feel shutdowns are caused by overheating is because they happen always during a peak temperature
– DevSharkJun 28 at 12:48

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Sounds reasonable - the junction max temperatures of these CPUs are usually 100 degrees Celcius (you haven't specified which CPU you have). Are you reaching such a temperature? - If so, check the cooling solution on your CPU. I.e. are fans operating properly, are vents blocked, is the thermal paste intact, etc.
– jksoegaardJun 28 at 12:52

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It's a 2.8 GHz Intel Core i7. Yeah, I do reach 100 degrees. The fans seem to be working properly, but yeah, I'll try to open it up and blow compressed air to clean it up a bit.
– DevSharkJun 28 at 13:14

Good idea - it doesn't sound like a sensor failure - so you do have a cooling issue. Blocked vents, broken fan, dust, bad thermal paste, etc.
– jksoegaardJun 28 at 13:56

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That’s not true in my experience - nor is it according to what I have heard from others. MacBook Pros are definitely not supposed to overheat and abruptly turn off - that is a defect within the hardware of that specific laptop. It is not a design problem common to the MBP. Note that throttling is a different matter - common to laptops from all vendors.
– jksoegaardJun 28 at 18:28